Building a Suitable Generalized Autoregressive Conditional Heteroskedasticity Time Series Model: A Nigeria Net Migration Rate Application

This work focused to build a Suitable Generalized Autoregressive Conditional Heteroskedasticity model for solving net migration rate problem in Nigeria. Analyzing the 51 year annual data of Net Migration Rate (NMR), Crude Death Rate (CDR), Fertility Rate (FR), Inflation Rate (IR), Real Annual Gross Domestic Product (RAGDP), Population Growth Rate (PGR) and Exchange Rate (ER) with Econometric Views (EViews) version 12.0 statistical software, the data was first represented on a graph to show a historical pattern of the variables. A multiple regression analysis was carried out to ascertain the nature of relationship existing between NMR (dependent variable) and ER, IR, CDR, PGR, FR and RAGDP as the independent variables. The results obtained showed a strong positive relationship and that the regression is not spurious. The series being Stationary was used for hypothesis testing, forecasting and fitting of time series models. With Augmented Dickey-Fuller (ADF) test, six series were stationary while with Kwiatkowski-Philips-Schmidt-Shin (KPSS) test, one was stationary. The Q-Statistics probability values were all greater than 0.5 across 36 – lags implying no ARCH models and residuals normally distributed. No autocorrelation, no heteroskedasticity and residuals normally distributed indicating that the GARCH family models studied with three error distributions can be employed to find the best model for solving migration rate problem in Nigeria. Normal Gaussian error distribution EGARCH (1, 1) performed best. The key measurable factors affecting NMR in Nigeria as observed in this work are ER, IR and PGR. Further studies should be done on both Normal Gaussian error distributions EGARCH from 2nd order, symmetric and asymmetric GARCH models to ascertain their performances in modeling Net Migration rate in Nigeria.